On the Physical Origins of the Millimeter Fundamental Plane in Active Galactic Nuclei

TL;DR

This work tests whether a compact, hot accretion flow around supermassive black holes can naturally explain the Millimeter Fundamental Plane (mmFP) linking $M_ullet$, $L_{mm}$, and $L_{X}$. Using five magnetically arrested disk (MAD) GRMHD simulations with dynamical magnetic fields, the authors perform general relativistic ray-tracing with grmonty to produce SEDs across a four-parameter grid ($M_ullet$, $\\dot m$, $a_ullet$, $R_ ext{high}$), assuming thermal electrons and including synchrotron, bremsstrahlung, and inverse Compton processes. They find that models with $10^{-6} \\\le \\\dot m \\\le 10^{-5}$ naturally reproduce the mmFP without fine-tuning, while lower accretion rates drift left due to optical-depth effects, and high-$\\dot m$ models can overshoot due to radiative cooling via IC; across the grid, X-rays are IC-dominated and show only a modest dependence on spin, while the millimeter emission is synchrotron-dominated and scales with $M_ullet$, $\\dot m$, and $R_ ext{high}$. The results imply that LLAGN mm and X-ray properties can be explained by compact MAD flows rather than extended jets, and they outline predictions for selection effects and the role of radiative cooling and non-thermal electrons in future work. This advances understanding of the physical origin of the mmFP and provides a framework for using horizon-scale imaging to constrain accretion physics near black holes.

Abstract

Observations of active galactic nuclei have revealed a correlation between millimeter luminosity, X-ray luminosity, and mass, suggesting the emission in each of these bands is powered by a common source. Starting with a set of five general relativistic magnetohydrodynamic simulations with dynamically important magnetic fields, we perform ray-tracing calculations to produce spectra including synchrotron emission, bremsstrahlung emission, and Compton scattering. Our models with similar Eddington ratios to the objects for which the relationship was inferred naturally reproduce observations without tuning. Our lower Eddington ratio models depart from this relationship, likely attributable to an observational bias against extremely low accretion rates. We find that inverse Compton scattering dominates the production of X-rays over bremsstrahlung radiation in almost all models, and in all models consistent with the observed correlation. We find only a modest spin dependence in this relationship. This study demonstrates that a compact, hot accretion flow with dynamically important magnetic fields can naturally explain observed millimeter and X-ray properties in low-luminosity active galactic nuclei. Future work should explore the impacts of non-thermal electron populations, weaker magnetic fields, and radiative cooling.

Figures (5)

• Figure 1: Comparison of our models with the "Millimeter Fundamental Plane" reported in Ruffa+2024. Each point represents one GRMHD simulation, color-coded by $\dot{m}$. The best fit from Ruffa+2024 is visualized with black lines, as well as the values from their primary sample of AGN. We find that our GRMHD models with $\log \dot{m} \lesssim -7$ drift to the left of the relation. Models with $\dot{m}=10^{-4}$, shown here as gray circles, were almost all found to have $\epsilon_{\rm rad} \gg 0.1$; these are excluded from future analysis.
• Figure 2: Spectral energy distributions as a function of Eddington ratio $\dot{m}$ and $R_{\rm high}$ with fixed spin, $a_{\bullet}$=+0.94. Models with $M_{\rm BH} = 10^9 M_\odot$ are shown in the top row, and models with $M_{\rm BH} = 10^6 M_\odot$ are shown in bottom row.
• Figure 3: A grid of time-averaged normalized total spectra as a function of two parameters, Eddington ratio $\dot{m}$, spin $a_{\bullet}$, with fixed $R_{high}=40$. Models with $M_{\rm BH} = 10^9 M_\odot$ are shown in the top row, and models with $M_{\rm BH} = 10^6 M_\odot$ are shown in bottom row respectively.
• Figure 4: Top: Fraction of model snapshots which satisfy mmFP as a function of $R_\mathrm{high}$, Eddington ratio $\dot{m}$ and spin. Bottom: Distribution of $\log(L_{\rm IC}/L_{\rm bremss})$ for all models in grey, compared to those consistent with the mmFP in orange.
• Figure 5: Proposed impact of selection effects. In the leftmost panel, we compare our GRMHD models to the observational sample from Ruffa+2024, color-coded by $\dot{m}$. For a given $L_{mm}$ and $M_\bullet$, the Ruffa+2024 sample generally overlaps with our models in $\dot{m}$, suggesting that our models are producing reasonable millimeter luminosities. The Ruffa+2024 sample only includes objects roughly above the dashed black line. If we restrict our models to those above this line, we find much better agreement with the mmFP in the right panel. This suggests that objects should drift to the left of the mmFP at lower accretion rates, as the synchrotron turnover frequency moves to lower frequencies.